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Honors CCP PreCalc (Drumm) > Trigonometric Identities > Flashcards

Trigonometric Identities Flashcards

1
Q

Reciprocal Identity
sinu =

A

= 1/cscu

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2
Q

Reciprocal Identity
cosu =

A

= 1/secu

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3
Q

Reciprocal Identity
tanu =

A

= 1/cotu

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4
Q

Reciprocal Identity
cscu =

A

= 1/sinu

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5
Q

Reciprocal Identity
secu =

A

= 1/cosu

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6
Q

Reciprocal Identity
cotu =

A

= 1/tanu

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7
Q

Quotient Identity
tanu =

A

= sinu/cosu

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8
Q

Quotient Identity
cotu =

A

= cosu/sinu

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9
Q

Pythagorean Identity
sin^2u + cos^2u =

A

= 1

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10
Q

Pythagorean Identity
tan^2u + 1 =

A

= sec^2u

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11
Q

Pythagorean Identity
1+ cot^2u =

A

= csc^2u

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12
Q

Cofunction Identity
sin(π/2 - u) =

A

= cosu

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13
Q

Cofunction Identity
cos(π/2 - u) =

A

= sinu

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14
Q

Cofunction Identity
tan(π/2 - u) =

A

= cotu

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15
Q

Cofunction Identity
cot(π/2 - u) =

A

= tanu

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16
Q

Cofunction Identity
csc(π/2 - u) =

A

= secu

17
Q

Cofunction Identity
sec(π/2 - u) =

A

= cscu

18
Q

Even/Odd Identity
sin(-u) =

A

= -sinu

19
Q

Even/Odd Identity
csc(-u) =

A

= -cscu

20
Q

Even/Odd Identity
cos(-u) =

A

= cosu

21
Q

Even/Odd Identity
sec(-u) =

A

= secu

22
Q

Even/Odd Identity
tan(-u) =

A

= -tanu

23
Q

Even/Odd Identity
cot(-u) =

A

= -cotu

24
Q

Sum & Difference Formula
sin(u +- v) =

A

= sinucosv +- cosusinv

25
Q

Sum & Difference Formula
cos(u +- v) =

A

= cosucosv -+ sinusinv

26
Q

Sum & Difference Formula
tan(u +- v) =

A

= (tanu +- tanv)/(1 -+ tanutanv)

27
Q

Double-Angle Formula
sin2u =

A

= 2sinucosu

28
Q

Double-Angle Formula
cos2u =

A

= cos^2u - sin^2u
= 2cos^2u - 1
= 1 - 2sin^2u

29
Q

Double-Angle Formula
tan2u =

A

= (2tanu)/(1 - tan^2u)

30
Q

Half-Angle Formula
sin(u/2) =

A

= +- √(1 - cosu)/2

31
Q

Half-Angle Formula
cos(u/2) =

A

= +- √(1 + cosu)/2

32
Q

Half-Angle Formula
tan(u/2) =

A

= (1 - cosu)/sinu
= sinu/(1 + cosu)

33
Q

Power-Reducing Formula
sin^2u =

A

= (1 - cos2u)/2

34
Q

Power-Reducing Formula
cos^2u =

A

= (1 + cos2u)/2

35
Q

Power-Reducing Formula
tan^2u =

A

= (1 - cos2u)/(1 + cos2u)

36
Q

If a nonvertical line has inclination @ and slope m, then…

A

m = tan@

37
Q

Finding an angle between two lines with slopes m1 and m2

A

tan@ = |(m1 - m2)/(1 + m1m2)|

38
Q

Distance between the point (x,y) and the line Ax + By + C = 0

A

d = |Ax1 + By1 + C|/(√A^2 + B^2)

Honors CCP PreCalc (Drumm) (1 decks)

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